Theoretical Model

This chapter describes shortly the theory of micro-polar hypoplasticity including a characteristic length of micro-structure in the form of a mean grain diameter. First, a non-polar hypoplastic constitutive model formulated at Karlsruhe University by Gudehus (1996) and Bauer (1996) for mainly monotonic deformation paths is summarized. Some results of so-called element tests (oedometric compression, triaxial compression, cyclic simple shearing) by a hypoplastic constitutive model are presented for different initial void ratios and pressure levels. Next, the calibration procedure for hypoplasticity to determine material parameters given by Bauer (1996) and Herle and Gudehus (1999) is outlined. Later, the micro-polar (Cosserat) continuum is presented. The advantages of the micro-polar theory with respect to a conventional (non-polar) continuum to capture shear localization are outlined. The equations of a micro-polar constitutive law proposed by Tejchman (1997) are given which were obtained by enhancement of a non-polar hypoplastic constitutive law of Gudehus (1996) and Bauer (1996) by micro-polar quantities. Finally, the FE implementation of a micro-polar model in a quasi-static regime is depicted.